Analysis of Noisy Evolutionary Optimization When Sampling Fails

In noisy evolutionary optimization, sampling is a common strategy to deal with noise. By the sampling strategy, the fitness of a solution is evaluated multiple times (called \emph{sample size}) independently, and its true fitness is then approximated by the average of these evaluations. Previous studies on sampling are mainly empirical. In this paper, we first investigate the effect of sample size from a theoretical perspective. By analyzing the (1+1)-EA on the noisy LeadingOnes problem, we show that as the sample size increases, the running time can reduce from exponential to polynomial, but then return to exponential. This suggests that a proper sample size is crucial in practice. Then, we investigate what strategies can work when sampling with any fixed sample size fails. By two illustrative examples, we prove that using parent or offspring populations can be better. Finally, we construct an artificial noisy example to show that when using neither sampling nor populations is effective, adaptive sampling (i.e., sampling with an adaptive sample size) can work. This, for the first time, provides a theoretical support for the use of adaptive sampling

Uncertainty And Evolutionary Optimization: A Novel Approach

Evolutionary algorithms (EA) have been widely accepted as efficient solvers for complex real world optimization problems, including engineering optimization. However, real world optimization problems often involve uncertain environment including noisy and/or dynamic environments, which pose major challenges to EA-based optimization. The presence of noise interferes with the evaluation and the selection process of EA, and thus adversely affects its performance. In addition, as presence of noise poses challenges to the evaluation of the fitness function, it may need to be estimated instead of being evaluated. Several existing approaches attempt to address this problem, such as introduction of diversity (hyper mutation, random immigrants, special operators) or incorporation of memory of the past (diploidy, case based memory). However, these approaches fail to adequately address the problem. In this paper we propose a Distributed Population Switching Evolutionary Algorithm (DPSEA) method that addresses optimization of functions with noisy fitness using a distributed population switching architecture, to simulate a distributed self-adaptive memory of the solution space. Local regression is used in the pseudo-populations to estimate the fitness. Successful applications to benchmark test problems ascertain the proposed method's superior performance in terms of both robustness and accuracy.Comment: In Proceedings of the The 9th IEEE Conference on Industrial Electronics and Applications (ICIEA 2014), IEEE Press, pp. 988-983, 201

Differentially Private Adaptive Optimization with Delayed Preconditioners

Privacy noise may negate the benefits of using adaptive optimizers in differentially private model training. Prior works typically address this issue by using auxiliary information (e.g., public data) to boost the effectiveness of adaptive optimization. In this work, we explore techniques to estimate and efficiently adapt to gradient geometry in private adaptive optimization without auxiliary data. Motivated by the observation that adaptive methods can tolerate stale preconditioners, we propose differentially private adaptive training with delayed preconditioners (DP^2), a simple method that constructs delayed but less noisy preconditioners to better realize the benefits of adaptivity. Theoretically, we provide convergence guarantees for our method for both convex and non-convex problems, and analyze trade-offs between delay and privacy noise reduction. Empirically, we explore DP^2 across several real-world datasets, demonstrating that it can improve convergence speed by as much as 4x relative to non-adaptive baselines and match the performance of state-of-the-art optimization methods that require auxiliary data.Comment: Accepted by ICLR 202